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The definition of $V_{S1}$ is

the stalling speed or the minimum steady flight speed obtained in a specific configuration

from 14 CFR §1.2 Abbreviations and symbols.

Why is this vague in terms of the configuration?

My understanding is that $V_{S1}$ is in terms of flaps retracted but this can't be gleaned from the definition.

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Typically, such wording means that the "specific configuration" must be stipulated when the designation is actually used. That is, it may depend on the context.

Indeed, in the body of the document we see for "Light-sport aircraft" (emphasis mine):

A maximum stalling speed or minimum steady flight speed without the use of lift-enhancing devices ($V_{S1}$) of not more than 45 knots CAS at the aircraft's maximum certificated takeoff weight and most critical center of gravity.

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